A problem for the alternative difference measure of confirmation

Abstract

Among Bayesian confirmation theorists, several quantitative measures of the degree to which an evidential proposition E confirms a hypothesis H have been proposed. According to one popular recent measure, s, the degree to which E confirms H is a function of the equation P(H|E) − P(H|~E). A consequence of s is that when we have two evidential propositions, E1 and E2, such that P(H|E1) = P(H|E2), and P(H|~E1) ≠ P(H|~E2), the confirmation afforded to H by E1 does not equal the confirmation afforded to H by E2. I present several examples that demonstrate the unacceptability of this result, and conclude that we should reject s (and other measures that share this feature) as a measure of confirmation.

Keywords

Notes

Acknowledgments

This paper had its genesis in a graduate seminar on probability at Western Michigan University in Fall 2009. I am grateful to Timothy McGrew for teaching that class and helping me think through these issues. I would also like to thank David Christensen for insightful correspondence on this project, as well as Matthew Lee and an anonymous reviewer for helpful comments on earlier drafts.